Limit analysis and convex programming: A decomposition approach of the kinematic mixed method

Abstract

This paper proposes an original decomposition approach to the upper bound method of limit analysis. It is based on a mixed finite element approach and on a convex interior point solver using linear or quadratic discontinuous velocity fields. Presented in plane strain, this method appears to be rapidly convergent, as verified in the Tresca compressed bar problem in the linear velocity case. Then, using discontinuous quadratic velocity fields, the method is applied to the celebrated problem of the stability factor of a Tresca vertical slope: the upper bound is lowered to 3.7776-value to be compared with the best published lower bound 3.772-by succeeding in solving non-linear optimization problems with millions of variables and constraints. Copyright (C) 2008 John Wiley & Sons, Ltd